Is there a way to bake ambient occlusion map as strong as in viewport shading ambient occlusion?
The viewport AO uses different engine than the bake AO function (Blender Internal or Cycles in 2.79 Blender), so the settings for the viewport AO are not used in the Bake.

The viewport AO is multiplied by 5, so if you take your baked AO into Photoshop or another editor and you play with the levels of the image (or you multiply 5 these images on top of each other) you get similar result.

Selected to Active does not have impact on the strength of AO, only from which object it will get calculated.